178 



MICROPHONES 



parallel rigid plate. The electrical circuit of this microphone is shown in 

 Fig. 9.4. 

 The capacity, in statfarads, at any instant is given by 



Ce = Ceo + Cei sin co/ 



9.6 



where Ceo = capacity in the absence of an applied pressure, in statfarads, 

 Cei = maximum change in the capacity due to the external applied 

 sinusoidal pressure, in statfarads, 

 CO = 271/, and 

 / = frequency, in cycles per second. 



SCREEN 

 DIAPHRAGM 





-CLAMPING RING 

 CROSS-SECTIONAL VIEW 



1000 



FREQUENCY 



Fig. 9.4. Cross-sectional view of a condenser microphone. The electrical circuit shows the 

 microphone connected to a vacuum tube. The graph shows the open circuit voltage re- 

 sponse frequency characteristics. B. Response in free space. A. Response for constant 

 sound pressure on the diaphragm. 



From the electrical circuit 



eo — VEt 



Ce *j 



dt 



9.7 



where eo = polarizing voltage, in statvolts, 



rE = resistance of the bias resistor, in statohms, 

 t = current, in statamperes, and 

 / = time, in seconds. 

 Equation 9.7 assumes that the bias resistor Teb and the input impedance 

 of the vacuum tube is very large compared with r^. Then ^o may be con- 

 sidered to be in series with Ceo and r^. Substituting the value of Ce from 

 equation 9.7 in equation 9.6 and differentiating 



di 

 (Ceo + Cei sin c>:t)rE — + (1 + VeCeio^ cos oit)i — eoCsi^ cos co/ = 9.8 

 at 



